The family of a Brooklyn woman who bled to death, and the paramedics who tried to save her, have charged that firefighters who arrived first made a halfhearted effort to find the woman – losing precious minutes that might have saved her life.

Responding to a 911 call, firefighters with Engine Company 214 in Bedford-Stuyvesant knocked on a neighbor’s door, then “sat outside in the truck” while Muriel Holloway, 70, lay bleeding in her apartment, her family says.

After furious paramedics with Battalion 38 filed a complaint about the May 11 death, the FDNY cleared the firefighters of any wrongdoing.

“They did all they could,” said spokesman Frank Gribbon.

But the Holloway family wants another investigation and filed a complaint with the state Health Department last week. .

“I keep thinking if someone else was here quicker, my mother could still be here,” said son Elliot Holloway, 54, who was visiting for Mother’s Day when Muriel collapsed.

Firefighters are trained as first responders for medical emergencies because they can get to patients first. But paramedics gripe that the Bravest often drag their feet on medical calls.

“Their job is to fight fires,” said a source familiar with FDNY and EMS operations. “The medical thing is almost a burden to them.”

Muriel – a grandmother of nine – had undergone kidney dialysis for 13 years. That night, a treatment valve implanted in her arm opened, causing heavy bleeding. She collapsed in her fourth-floor bedroom.